Recently the interest in realizing topological phases by artificial systems has been actively broadened into 4D topological phases. Here we present a faithful realization of 4D topological insulator with time-reversal symmetry in class AI, using electric circuits with periodic connectivity in four dimensions. The experimental realizability is strongly supported by a software simulation of the electric circuit, where the double Weyl boundary states as the characteristic of the topological phase are in precise agreement with the theoretical prediction. Compared with existing schemes for realizing high-dimensional topological phases by low-dimensional systems with some synthetic dimensions, all of four dimensions are faithfully emulated on an equal footing, making the Weyl states on boundaries along all directions experimentally accessible. Moreover, the time-reversal symmetry permitting the topological phase is intrinsic for the electric circuit described by the Kirchhoff equations, rather than various simulation schemes for 2D and 3D topological insulators in class AII with finite-tunings for time-reversal symmetry.